Abstract

High lateral resolution ($\sim 5\,\,{\unicode{x00B5}}\rm m$) optical coherence tomography (OCT) that employs a variable cross-cylinder (VCC) to compensate for astigmatism is presented for visualizing minute structures of the human retina. The VCC and its sensorless optimization process enable ocular astigmatism correction of up to ${-}{5.0}$ diopter within a few seconds. VCC correction has been proven to increase the signal-to-noise ratio and lateral resolution using a model eye. This process is also validated using the human eye by visualizing the capillary network and human cone mosaic. The proposed method is applicable to existing OCT, making high lateral resolution OCT practical in clinical settings.

© 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

1. INTRODUCTION

Optical coherence tomography (OCT) is one of the most widely adopted modalities to diagnose the eye in clinical settings, enabling us to acquire structural and functional information from the eye [1]. The spatial resolution of OCT is defined independently in the axial and lateral directions. Commercially available ophthalmic OCT systems typically have approximately 6 µm axial and 15 µm lateral resolutions. To further improve the axial resolution of OCT, a light source with a broader optical bandwidth should be used. On the other hand, to improve the lateral resolution of OCT, a probe beam with a larger beam diameter must be incident to the eye. However, in addition to the limitation of the effective pupil diameter of the human eye, the effects of ocular aberrations, including higher-order modes, become unignorable as the beam diameter increases [2,3]. Thus, commercial ophthalmic OCT systems typically adopt a beam diameter (${{1/e}^2}$ width) of less than 1.5 mm at the pupil of the measured eye. Adaptive optics (AO) is undoubtedly the best and most mature method to mitigate the effects of ocular aberrations [4]. Several studies have been conducted, and the significance of aberration correction in high lateral resolution retinal OCT imaging has been rigorously verified with a large beam diameter of ${\sim}{6}\;{\rm mm}$ [58]. Combined with the wavefront sensor, additional devices such as deformable mirror/lens or liquid crystal devices have been employed as aberration compensators in AO systems [2,9,10]. Although these devices enable precise correction of ocular aberrations including higher-order modes, AO systems have not been widely used in clinical practice for a number of reasons, including large footprint, higher cost, and narrow field of view (FOV).

As an alternative approach, OCT systems with a moderate beam diameter (3–4 mm) have been proposed [11]. In combination with a 6 µm axial resolution, a 3–4 mm beam diameter provides a ${\sim}{6}\;\unicode{x00B5}{\rm m}$ near-isotropic resolution. Note that this lateral resolution is an approximately ${2} \times$ worse resolution than that of high-performance AO systems and more than ${2} \times$ better resolution than that of commercial ophthalmic OCT systems. In fact, cellular-level OCT imaging has been demonstrated using this approach, although the imaging target was limited to eyes with lower-order aberrations. According to the literature, the average pupil diameter of a 70 year old human is ${\sim}{3}\;{\rm mm}$ in a darkroom environment under nonmydriatic conditions [12]. In addition, lower-order aberrations, i.e., defocus and astigmatism, are dominant, and higher-order aberrations are ignorable in this beam diameter range [3]. Nevertheless, defocus is corrected by the instrument’s focusing system, and the ability to correct astigmatism is typically not yet included in OCT systems. As previously mentioned, several devices have been proposed as aberration compensators. Among them, a variable cross-cylinder (VCC, or Stokes lenses), an embodiment of the Alvarez lens [13,14] comprising a pair of cylindrical lenses, can compensate for astigmatism without sacrificing the OCT system FOV. Moreover, this device is relatively low cost and can fine-tune its aberration coefficients; it is therefore considered to have significant potential in clinical practice [1517].

 figure: Fig. 1.

Fig. 1. Schematic of (a) the OCT sample arm, which equips a VCC and (b) the rotation angles ${A_{\rm VCC1}}$, ${A_{\rm VCC2}}$, and ${A_{{\rm VCC}}}$. The astigmatism generated by the VCC is determined by the rotation angles and cylindricities of two lenses. The VCC was placed in a pupil conjugate plane and relayed to the pupil at a magnification ($\beta$).

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 figure: Fig. 2.

Fig. 2. Contour plots of the squared total cylindrical power ($C_{{\rm total}}^2$) calculated as a function of ${C_{{\rm VCC}}}$ and ${A_{{\rm VCC}}}$ in the cases where ($C_{{\rm eye}}$, ${A_{{\rm eye}}}$) = (a) (${-}{0.5}\;{\rm D}$, 135 deg); (b) (${-}{2.0}\;{\rm D}$, 180 deg); and (c) (${-}{5.0}\;{\rm D}$, 45 deg).

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In this study, we estimate and correct ocular astigmatism without wavefront sensors based on the sensorless AO method [9,18,19], where well-resolved imaging was achieved by simply adding the VCC to the optical system. The proposed system enables resolving retinal microstructures that cannot be clearly imaged by current commercial OCT systems (e.g.,  photoreceptor cells, retinal nerve fibers, retinal capillaries [20]) under nonmydriatic conditions with a reasonable FOV. To the best of the authors’ knowledge, astigmatism correction using a VCC and its sensorless optimization for retinal OCT imaging has been demonstrated for the first time, offering a promising method to achieve higher lateral resolution for practical use. The following sections discuss the principle of astigmatism correction using VCC, the evaluation and imaging results using a static model eye sample, and the applicability to retinal imaging of the human eye.

2. PRINCIPLE OF ASTIGMATISM CORRECTION USING VCC

A VCC comprises a couple of cylindrical lenses with norm-equal but sign-opposite cylindrical powers, as illustrated in Fig. 1(a). It is placed near the pupil conjugate and relayed to the pupil plane of the measured eye at a magnification ($\beta$). With this configuration, the cylindrical power and axis (hereinafter referred to as ${C_{{\rm VCC}}}$ and ${A_{{\rm VCC}}}$, respectively) are generated by rotating the angle of each cylindrical lens and are determined using the following equations [21]:

$$\begin{split}{C_{{\rm VCC}}} &= \frac{{2{C_{\rm VCC1}}}}{{{\beta ^2}}}\cos \left({{A_{\rm VCC2}} - {A_{\rm VCC1}}} \right)\\{A_{{\rm VCC}}}& = \frac{{{A_{\rm VCC1}} + {A_{\rm VCC2}}}}{2},\end{split}$$
where ${C_{\rm VCC1}}$ and ${C_{\rm VCC2}}({\approx - {C_{\rm VCC1}}})$ are the power, and ${A_{\rm VCC1}}$ and ${A_{\rm VCC2}}$ [Fig. 1(b)] are the rotation angles of the cylindrical lenses.

In addition, the total cylindrical power $C_{{\rm total}}$ resulting from the VCC and measured eye is given as follows [21]:

$$\begin{split}C_{{\rm total}}^2 &= {\left({C_{{\rm eye}}\cos 2{A_{{\rm eye}}} - {C_{{\rm VCC}}}\cos 2{A_{{\rm VCC}}}} \right)^2} \\&\quad + {\left({C_{{\rm eye}}\sin 2{A_{{\rm eye}}} - {C_{{\rm VCC}}}\sin 2{A_{{\rm VCC}}}} \right)^2}\\ &= {C_{{\rm VCC}}}^2 - 2{C_{{\rm VCC}}}C_{{\rm eye}}\cos 2\left({{A_{{\rm VCC}}} - {A_{{\rm eye}}}} \right) + C_{{\rm eye}}^2,\end{split}$$
where $C_{{\rm eye}}$ and ${A_{{\rm eye}}}$ are the cylindrical power and axis of the eye, respectively. $C_{{\rm total}}^2$ is a sinusoidal function of ${A_{{\rm VCC}}}$ for a fixed ${C_{{\rm VCC}}}$ and is also a parabolic function of ${C_{{\rm VCC}}}$ for a fixed ${A_{{\rm VCC}}}$. Figure 2 shows a representative simulation result of $C_{{\rm total}}^2$ as a function of ${C_{{\rm VCC}}}$ and ${A_{{\rm VCC}}}$. The dark blue points on the maps indicate the optimal values of ${C_{{\rm VCC}}}$ and ${A_{{\rm VCC}}}$ for correcting astigmatism of the eye (i.e., $C_{{\rm total}} = {0}$). The vertical and horizontal line profiles across the coordinate of $C_{{\rm total}} = {0}$ are also shown.

3. FUNDAMENTAL EVALUATION

The VCC was implemented in a swept-source OCT prototype (Topcon Corp.). A microelectromechanical system tunable laser was used as the light source. The laser light source has a center wavelength of approximately 1050 nm, a wavelength sweeping range of more than 100 nm, and an A-scan rate of 400 kHz. The average input power at the pupil was set to 4.0 mW. The ${{1/e}^2}$ beam diameter was set to 3.0 mm to avoid higher-order aberrations and to account for the pupil diameter of elderly people. The resulting axial and lateral resolutions in the tissue were 8.0 and 5.5 µm, respectively. The axial resolution was assessed by measuring the full width at half-maximum of the axial point spread function (PSF) using a mirror target, while the lateral resolution was assessed by measuring the line profile of OCT en face image of USAF-1951 resolution target (Edmund Optics, Negative, 1951 USAF Hi-Resolution Target) using the Rayleigh resolution criteria. The VCC, which has a cylindrical power of approximately ${\pm}0.75$ diopter (D), was placed near the pupil conjugate and relayed to the pupil with a magnification $\beta$ of 0.47. Therefore, astigmatism up to ${\pm}6.95\,\rm D$ can be compensated. Because positive values of astigmatism can be converted to negative values by rotating the reference axis to the orthogonal axis, hereinafter, only negative astigmatism will be considered, which is used in most eyeglass prescriptions. The air gap between the two cylindrical lenses was set to 1 mm. Both lenses were antireflection (AR)-coated with a reflectance of less than 0.05% over the entire wavelength of the light source. The two cylindrical lenses integrated in the VCC were motor-controlled independently with a rotation speed of 150 deg/s. According to the sensorless AO method, the OCT image quality score was used as the merit function for VCC optimization. In this study, we used brightness (i.e., the mean value of the OCT signal intensity) as the merit function, which was calculated from OCT B-scan images captured with a circular scan (scan diameter = 1.2 mm, resolution = 136 measurement points/mm) centered on the imaging center. The scan pattern was selected to include all meridians and to enable fast scanning.

For correcting astigmatism, it is necessary to identify the coordinates corresponding to $C_{{\rm total}} = {0}$ mentioned above. According to Eq. (2), the two consecutive steps described below will lead to the global minimum of $C_{{\rm total}}$. First, ${A_{{\rm VCC}}}$ is scanned in a range from 0 to 180 deg with constant ${C_{{\rm VCC}}}$ (${C_c}$), and the ${A_{{\rm VCC}}}$ that maximizes the merit function is recorded as ${A_{{\rm opt}}}$. Then, ${C_{{\rm VCC}}}$ is scanned in a certain range with ${A_{{\rm opt}}}$, and the ${C_{{\rm VCC}}}$ that maximizes the merit function is recorded as ${C_{{\rm opt}}}$. The ${A_{{\rm opt}}}$ and ${C_{{\rm opt}}}$ determined by this VCC optimization process should compensate for the astigmatism of the measured eye. To validate the performance of VCC optimization processes, three types of astigmatic model eyes with ($C_{{\rm eye}}$, ${A_{{\rm eye}}}$) = (${-}{0.5}\;{\rm D}$, 135 deg), (${-}{2.0}\;{\rm D}$, 180 deg), and (${-}{5.0}\;{\rm D}$, 45 deg) were used. The model eye has a focal length of 17 mm and a layer comprising 8 µm microbeads (Micropearl SP-208, Sekisui Chemical Co. Ltd.) encapsulated in a base silicone rubber (FRV138, Momentive GmbH) with 70 µm thickness at around the focal position, mimicking the fundus retina of the human eye. It also has a cylindrical trial lens placed 12 mm from its corneal vertex. This means that we can change the cylindrical power and axis arbitrarily by changing the power and axis of the trial lens.

Figure 3 shows how the merit functions transit in the VCC optimization processes for each model eye. In each case, ${C_c}$ was first set to ${-}{1.5}\;{\rm D}$, and ${A_{{\rm VCC}}}$ was scanned from 0 to 180 deg at 5 deg intervals. Next, ${A_{{\rm VCC}}}$ was set to the ${A_{{\rm opt}}}$ (red symbol) and ${C_{{\rm VCC}}}$ was scanned from approximately 0.0 to ${-}{7.0}\;{\rm D}$ at approximately 0.2 D intervals. For each model eye, the merit function around the peak position behaved sinusoidally during ${A_{{\rm VCC}}}$ searching and parabolically during ${C_{{\rm VCC}}}$ searching, which is consistent with the cross sections shown in Fig. 2. The discrepancy between the expected and observed behavior in the region away from the peak position was not analyzed in this study, but it indicates that there is nonlinearity between $C_{{\rm total}}^2$ and the merit function. Note that the higher the astigmatic power, the larger the change in the merit function.

 figure: Fig. 3.

Fig. 3. Outputs of the merit function as a function of scanning the cylindrical axis ${A_{{\rm VCC}}}$ from 0 deg to 180 deg and the cylindrical power ${C_{{\rm VCC}}}$ approximately from 0 to ${-}{7.0}\;{\rm D}$ for three types of astigmatic model eyes. (a) ($C_{{\rm eye}}$, ${A_{{\rm eye}}}$) = (${-}{0.5}\;{\rm D}$, 135 deg); (b) ($C_{{\rm eye}}$, ${A_{{\rm eye}}}$) = (${-}{2.0}\;{\rm D}$, 180 deg); and (c) ($C_{{\rm eye}}$, ${A_{{\rm eye}}}$) = (${-}{5.0}\;{\rm D}$, 45 deg). In each case, first, ${A_{{\rm VCC}}}$ was scanned with fixed set of ${C_c} = - {1.5}\;{\rm D}$. ${A_{{\rm VCC}}}$ value that maximizes the merit function (${A_{{\rm opt}}}$) are indicated in red and arrows. Subsequently, ${C_{{\rm VCC}}}$ was scanned with the fixed parameter of the ${A_{{\rm opt}}}$. ${C_{{\rm VCC}}}$ value that maximizes the merit function (${C_{{\rm opt}}}$) are indicated in light blue and arrows.

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 figure: Fig. 4.

Fig. 4. Scatterplots of the correlation between the trial lens setting on the model eye ($C_{{\rm eye}}$, ${A_{{\rm eye}}}$) and the value obtained by the VCC optimization process (${C_{{\rm opt}}}$, ${A_{{\rm opt}}}$) for (a) cylindrical power and (b) cylindrical axis. The dashed lines indicate the ideal values.

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 figure: Fig. 5.

Fig. 5. Variations in the relative SNR of the OCT signal. The relative SNR with VCC is set to 0 at the point $C_{{\rm eye}} = {0.0}\;{\rm D}$. The dashed line shows the linear relationship between cylindrical power and relative SNR with a slope ${-}{4.4}$.

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 figure: Fig. 6.

Fig. 6. OCT images of the microbeads model eye. (a) OCT B-scan image of a model eye; (b)–(d) comparison between OCT en face projections (${1}\;{\rm mm} \times {1}\;{\rm mm}$, ${512}\;{\rm pixels} \times {512}\;{\rm pixels}$) of the microbeads layer when ${C_{{\rm VCC}}} = {0}$ (VCC OFF) and after VCC astigmatism correction (VCC ON). The refractive properties of the model eye are (b) (${-}{0.5}\;{\rm D}$, 135 deg); (c) (${-}{2.0}\;{\rm D}$, 180 deg); and (d) (${-}{5.0}\;{\rm D}$, 45 deg). Bar: 200 µm.

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To verify the accuracy of the VCC optimization process, the correlations between ${C_{{\rm opt}}}$ and $C_{{\rm eye}}$ and between ${A_{{\rm opt}}}$ and ${A_{{\rm eye}}}$ were quantified, as illustrated in Fig. 4. We used model eyes with $C_{{\rm eye}}$ from 0.0 to ${-}{5.0}\;{\rm D}$ at 0.5 D intervals, and ${A_{{\rm eye}}}$ from 0 to 135 deg at 45 deg intervals. For each astigmatic model eye, VCC optimization was iteratively executed 10 times. The resulting correlation coefficients were 0.99 (${ p} \lt {0.01}$) for both cylindrical power and axis. These substantial correlations suggest that a VCC-equipped OCT can correct and simultaneously measure the cylindrical properties of the measured eye. The standard deviations of residual differences were 0.18 D for cylindrical power and 6 deg for the cylindrical axis.

Next, we quantitatively examined the significance of astigmatism correction on the OCT signal-to-noise ratio (SNR) [22] using the astigmatic model eyes, which have a mirror instead of the retina-mimicking layer. As mentioned above, the cylindrical property of the model eye can be changed arbitrarily by changing the trial lens set in front of the model eye. During the measurement, OCT beam scanning was stopped, and the PSF was recorded. Figure 5 shows how the SNR of the PSF was improved by VCC astigmatism correction. When the VCC unit was completely removed from the OCT system, the SNR decreased monotonically as the cylindrical power of the trial lens increased. By contrast, the SNRs were maintained at almost constant values with VCC astigmatism correction. A linear relationship with a slope of ${-}{4.4}\;{\rm dB/D}$ was obtained between cylindrical power and relative SNR, which manifests the importance of astigmatism correction for high-resolution retinal OCT imaging.

To evaluate the effectiveness of astigmatism correction in retinal OCT imaging, OCT images of the astigmatic model eye containing the microbeads layer mentioned above were captured before and after astigmatism correction and compared. Figure 6(a) shows an OCT B-scan image of the model eye. The retina-mimicking microbead layer is highlighted in orange. The OCT en face projections generated from the microbead layer are shown in Figs. 6(b)–6(d). The microbead images in Figs. 6(b)–6(d) are blurred when ${C_{{\rm VCC}}} = {0}$ (VCC OFF) owing to the astigmatism, and each microbead could not be resolved. By contrast, after VCC astigmatism correction, each microbead with a diameter of 8 µm was clearly resolved.

 figure: Fig. 7.

Fig. 7. (a), (b) Data set for the astigmatic eye of ($C_{{\rm eye}}$, ${A_{{\rm eye}}}$) = (${-}{1.6}\;{\rm D}$, 104 deg). (a) Changes in merit function during the search for ${A_{{\rm opt}}}$ and ${C_{{\rm opt}}}$ in the astigmatic human eye; (b) OCTA images (${3}\;{\rm mm} \times {3}\;{\rm mm}$, ${512}\;{\rm pixels} \times {512}\;{\rm pixels}$, five repetitions) of the superficial layer captured when ${C_{{\rm VCC}}} = {0}$ (VCC OFF) and after VCC astigmatism correction (VCC ON). (c), (d) Data set for the astigmatic eye of ($C_{{\rm eye}}$, ${A_{{\rm eye}}}$) = (${-}{4.3}\;{\rm D}$, 99 deg) obtained in the same manner. Bar: 200 µm.

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4. OCT IMAGING OF ASTIGMATIC HUMAN EYES

We conducted two experiments on human eyes in vivo using the VCC-equipped OCT prototype device. To accelerate and simplify the routine use of VCC-equipped OCT devices for healthcare practitioners, we carefully selected the parameter settings for the VCC optimization process mentioned in Section 3. We set the ${A_{\rm opt}}$ searching range from approximately 135 deg to 315 deg with a step of 10 deg, and set ${{C}_c}$ to ${-}{1.5}\;{\rm D}$. Because cylindrical axes around 180 deg or 90 deg (i.e., with-the-rule and against-the-rule astigmatism, respectively) are dominant in the population [23,24], we set it so that 180 deg and 90 deg are located inside, not on the edge, of the searching range. Next, we set the ${{C}_{{\rm opt}}}$ search range from approximately 0.0 to ${-}{6.0}\;{\rm D}$ with a step of 0.3 D. The ${{ C}_{{\rm opt}}}$ search range includes cylindrical powers of more than 95% of the eyes of the population [25]. The ${{C}_{{\rm opt}}}$ search was stopped when the merit function decreased 5 times in a row to avoid a time-consuming and redundant process. Finally, ${{A}_{{\rm opt}}}$ and ${{C}_{{\rm opt}}}$ were obtained by parabolic fitting of the measured merit functions, which improved the robustness with respect to noisy measurements.

 figure: Fig. 8.

Fig. 8. OCT images of the emmetropic human eye at a region 30 deg from the macular center. OCT B-scan with segmentation boundaries and OCT en face projections (${1}\;{\rm mm} \times {1}\;{\rm mm}$, ${512}\;{\rm pixels} \times {512}\;{\rm pixels}$) near the IS/OS junction when (a) ${C_{{\rm VCC}}} = {0}$ (VCC OFF) and (b) after VCC astigmatism correction (VCC ON). Bar: 200 µm.

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It has been explained that the eye with astigmatism may obscure the retinal microstructure even at the posterior pole region, specifically the capillary structure in the en face plane. To investigate the effectiveness of the VCC astigmatism correction in such cases, we acquired OCT angiography (OCTA) images around the macular region of a human eye before and after VCC astigmatism correction. The eye was emmetropic and wore the trial lens with two types of cylindrical glasses for mimicking astigmatic eyes. Figures 7(a), 7(b) and 7(c), 7(d) show the results in the case of (${{C}_{{\rm eye}}}$, ${{A}_{{\rm eye}}}$) = (${-}{1.6}\;{\rm D}$, 104 deg) and (${-}{4.3}\;{\rm D}$, 99 deg), respectively. The astigmatic properties were validated using a refractometer (KR-1W, Topcon Corp.). Figures 7(a) and 7(c) show variations in the merit function during the VCC optimization process, which were performed in 5.3 s and 6.9 s, respectively. The astigmatisms were estimated to (${{C}_{{\rm opt}}}$, ${{A}_{{\rm opt}}}$) = ($-{1.4}\;{\rm D}$, 103 deg) and (${-}{4.4}\;{\rm D}$, 98 deg), and the merit function was increased by 4% and 22%, respectively, through VCC optimization. This development is reflected in the SNR improvements shown in Fig. 5. To confirm the high lateral resolution achieved by the 3 mm beam diameter and VCC astigmatism correction, we compared OCTA images of the superficial layer as illustrated in Figs. 7(b) and 7(d). Some small vessels that cannot be visualized when ${{\rm C}_{{\rm VCC}}} = {0}$ appeared in the image after VCC astigmatism correction.

Even for emmetropic eyes, OCT images can be affected by astigmatism when the beam is incident to the eye with eccentricity [26]. The astigmatic power is larger than 1.0 D for an eccentricity of 30 deg [27]. To evaluate the astigmatism correction performance on such an area, we acquired an OCT image of an emmetropic eye around the temporal 30 deg region using a fixation target. The VCC optimization was completed in approximately 6 s, and the parameters (${{ C}_{{\rm opt}}}$, ${{A}_{{\rm opt}}}$) were obtained as (${-}{1.6}\;{\rm D}$, 95 deg). Figure 8 shows the acquired OCT B-scan images with the inner segment/outer segment (IS/OS) segmentation boundaries and reconstructed OCT en face projections of near the IS/OS junction before and after VCC astigmatism correction. The photoreceptor mosaic, which is not resolved well prior to the correction, is clearly visualized after the correction. This result demonstrated the significance of VCC astigmatism correction on peripheral OCT imaging of an emmetropic eye. In this case, the brightness was increased by 11%. The combination of the 3 mm beam diameter and VCC astigmatism correction successfully realized the visualization of a minute retinal structure.

5. DISCUSSION

In this study, we studied the feasibility of high lateral resolution retinal OCT imaging with VCC correction and sensorless optimization for a real-time astigmatism correction method. It is proven that integration of the VCC unit into the prototype OCT system enhances the signal level and recovers the lateral resolution. We first evaluated it on static model eye samples, as shown in Figs. 36. Subsequently, its applicability to human eye OCT imaging was demonstrated, as shown in Figs. 7 and 8. The results describe two important advantages of VCC astigmatism correction. The first is the reduction in blurs induced by astigmatism. In our experiments, astigmatism up to ${-}{5.0}\;{\rm D}$ was corrected successfully. Although small residual VCC optimization errors were confirmed as shown in Fig. 4, these are not critical and neglectable, particularly for OCT imaging, as presented in Figs. 68. A more remarkable astigmatism correction effect appeared in en face OCT images. A previous study reported that a photoreceptor mosaic can be visualized in en face OCT images using a 200 kHz and 3 mm beam diameter OCT system [28]. The result presented in Fig. 8 shows further improvement in the visualization performance compared to the literature. Moreover, the imaging results in Figs. 68 suggest that ${-}{2.0}\;{\rm D}$ astigmatism significantly changes the OCT images. En face-based quantitative parameters such as “vessel density” calculated from OCTA could be also significantly changed by astigmatism, which can be compensated for by the VCC. Another important advantage of VCC astigmatism correction is the enhancement of the photon-collection yield. The retina and end tip of the fiber are set as optically conjugated. If there is astigmatism involved, the PSF at the fiber will be blurred, leading to coupling loss and reduced photon-collection efficiency. As a result, the SNR of the OCT image decreases, and subtle image contrast is hampered by noise, which may present an obstacle for clinicians interpreting the OCT image. Although adding a VCC to the optical systems requires four additional optical interfaces and induces a loss of approximately 4% of photon propagation, calculated based on the AR coating performance, appropriate astigmatic correction by the VCC ensures an increase in the photon-collection yield, as shown in Fig. 5. Here, the use of a 3 mm beam diameter, which is approximately twice the numerical aperture of commercial systems, also contributes to the improvement in photon collection.

The improvement by VCC can be expected in both light illumination and detection efficiency, that is, OCT signal intensity. Recently, computational AO (CAO), where blurs induced by aberrations are digitally removed via postprocessing, has attracted significant attention [29,30]. Although CAO is an attractive approach for aberration correction, the decrease in signal intensity due to aberrations cannot be recovered. In other words, CAO can possibly not achieve the same improvement in intensity as offered by traditional hardware-based AO methods. Thus, the combination of hardware-based aberration correction methods and CAO is a more desirable approach to constantly obtain diffraction-limited high-quality images [31]. Here, the hardware-based process compensates for the aberration in most parts and maximizes the OCT signal intensity; subsequently, CAO removes the residual aberrations including higher-order aberrations during postprocessing. It could be argued that, when the beam diameter is approximately 3 mm, CAO may not be considered necessary because the higher-order aberrations are ignorable. Further research is required to confirm this assumption.

As described above, VCC exhibits reasonable performance and is a low-cost device; it is expected to promote the commercialization of ophthalmic OCT devices with a high lateral resolution. Further, it can be implemented in devices with growing demands, namely ultrawide field OCT or far-peripheral OCT [32]. As the incident angles of OCT for the eye become wider, astigmatism becomes prominent and exceeds ${-}{2.0}\;{\rm D}$ at 40 deg eccentricity even for emmetropic eyes [33,34]. This is more significant in myopic eyes [35]. A VCC can also help improve the OCT image quality in these situations.

To constantly obtain a well-resolved image, the optimization error rate should be minimized. The errors may be caused by defocus and eye motions during the optimization and acquisition process. The errors caused by defocus were not investigated in this study; however, depth-resolved optimization [18] would be effective for preventing defocus issues. Moreover, fastening the optimization process reduces the motion errors. One solution might be the use of the premeasured refractive property of the measured eye as an initial value for VCC optimization. The optimization error rate must be examined in future clinical studies.

6. CONCLUSION

This study demonstrated a VCC-equipped ophthalmic OCT with a 3 mm beam diameter. The performance of the developed system was evaluated using astigmatic model eye samples. This fundamental study quantified the accuracy of the VCC astigmatism correction. In addition, the effectiveness of astigmatism correction with VCC has been confirmed on OCT imaging by examining the SNR performance. Finally, small retinal structures around the foveal region of an eye that mimics the astigmatic eye and at the peripheral region of an emmetropic human eye were successfully resolved in the OCT image after VCC astigmatism correction, demonstrating the need for astigmatism correction in high-resolution retinal OCT imaging.

Image quality is the cornerstone of most imaging modalities, and here, we have demonstrated OCT image quality enhancement by implementing a practical astigmatism correction method. To increase the applicability of this method, the optimization processing time must be improved. The feasibility and impact of VCC astigmatism correction on diseased eyes’ OCT imaging will be validated in future clinical studies.

Acknowledgment

The authors thank Dr. Y. Fukuma (SAI Corp.) for his fruitful discussions on this work.

Disclosures

The authors declare no conflicts of interest.

Data Availability

Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.

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14. W. E. Humphrey, “A remote subjective refractor employing continuously variable sphere-cylinder corrections,” Opt. Eng. 15, 154286 (1976). [CrossRef]  

15. J. Arines and E. Acosta, “Low-cost adaptive astigmatism compensator for improvement of eye fundus camera,” Opt. Lett. 36, 4164–4166 (2011). [CrossRef]  

16. J. A. Picazo-Bueno, M. Trusiak, and V. Micó, “Single-shot slightly off-axis digital holographic microscopy with add-on module based on beamsplitter cube,” Opt. Express 27, 5655–5669 (2019). [CrossRef]  

17. S. Ferrer-Altabás and V. Micó, “Characterization of a compact low-cost Stokes lens for astigmatism compensation in optical instruments,” Appl. Opt. 59, 3347–3352 (2020). [CrossRef]  

18. A. Camino, R. Ng, J. Huang, Y. Guo, S. Ni, Y. Jia, D. Huang, and Y. Jian, “Depth-resolved optimization of a real-time sensorless adaptive optics optical coherence tomography,” Opt. Lett. 45, 2612–2615 (2020). [CrossRef]  

19. J. Polans, B. Keller, O. M. Carrasco-Zevallos, F. LaRocca, E. Cole, H. E. Whitson, E. M. Lad, S. Farsiu, and J. A. Izatt, “Wide-field retinal optical coherence tomography with wavefront sensorless adaptive optics for enhanced imaging of targeted regions,” Biomed. Opt. Express 8, 16–37 (2017). [CrossRef]  

20. K. Zhou, S. Song, Q. Zhang, Z. Chu, Z. Huang, and R. K. Wang, “Visualizing choriocapillaris using swept-source optical coherence tomography angiography with various probe beam sizes,” Biomed. Opt. Express 10, 2847–2860 (2019). [CrossRef]  

21. N. A. Alpins, “A new method of analyzing vectors for changes in astigmatism,” J. Cataract Refractive Surg. 19, 524–533 (1993). [CrossRef]  

22. A. Agrawal, T. J. Pfefer, P. D. Woolliams, P. H. Tomlins, and G. Nehmetallah, “Methods to assess sensitivity of optical coherence tomography systems,” Biomed. Opt. Express 8, 902–917 (2017). [CrossRef]  

23. A. M. McKendrick and N. A. Brennan, “Distribution of astigmatism in the adult population,” J. Opt. Soc. Am. A 13, 206–214 (1996). [CrossRef]  

24. S. A. Read, S. J. Vincent, and M. J. Collins, “The visual and functional impacts of astigmatism and its clinical management,” Ophthal. Physiol. Opt. 34, 267–294 (2014). [CrossRef]  

25. N. Pontikos, S. Chua, P. J. Foster, S. J. Tuft, A. C. Day, and UK Biobank Eye and Vision Consortium, “Frequency and distribution of corneal astigmatism and keratometry features in adult life: methodology and findings of the UK Biobank study,” PLOS One 14, e0218144 (2019). [CrossRef]  

26. L. R. De Pretto, E. M. Moult, A. Y. Alibhai, O. M. Carrasco-Zevallos, S. Chen, B. Lee, A. J. Witkin, C. R. Baumal, E. Reichel, A. Z. de Freitas, J. S. Duker, N. K. Waheed, and J. G. Fujimoto, “Controlling for artifacts in widefield optical coherence tomography angiography measurements of non-perfusion area,” Sci. Rep. 9, 9096 (2019). [CrossRef]  

27. T. Liu and L. N. Thibos, “Interaction of axial and oblique astigmatism in theoretical and physical eye models,” J. Opt. Soc. Am. A 33, 1723–1734 (2016). [CrossRef]  

28. B. Potsaid, B. Baumann, D. Huang, S. Barry, A. E. Cable, J. S. Schuman, J. S. Duker, and J. G. Fujimoto, “Ultrahigh speed 1050 nm swept source/Fourier domain OCT retinal and anterior segment imaging at 100,000 to 400,000 axial scans per second,” Opt. Express 18, 20029–20048 (2010). [CrossRef]  

29. S. G. Adie, B. W. Graf, A. Ahmad, P. S. Carney, and S. A. Boppart, “Computational adaptive optics for broadband optical interferometric tomography of biological tissue,” Proc. Natl. Acad. Sci. USA 109, 7175–7180 (2012). [CrossRef]  

30. N. D. Shemonski, F. A. South, Y. Z. Liu, S. G. Adie, P. S. Carney, and S. A. Boppart, “Computational high-resolution optical imaging of the living human retina,” Nat. Photonics 9, 440–443 (2015). [CrossRef]  

31. F. A. South, K. Kurokawa, Z. Liu, Y. Z. Liu, D. T. Miller, and S. A. Boppart, “Combined hardware and computational optical wavefront correction,” Biomed. Opt. Express 9, 2562–2574 (2018). [CrossRef]  

32. N. Choudhry, J. Golding, M. W. Manry, and R. C. Rao, “Ultra-widefield steering-based spectral-domain optical coherence tomography imaging of the retinal periphery,” Ophthalmology 123, 1368–1374 (2016). [CrossRef]  

33. J. Polans, B. Jaeken, R. P. McNabb, P. Artal, and J. A. Izatt, “Wide-field optical model of the human eye with asymmetrically tilted and decentered lens that reproduces measured ocular aberrations,” Optica 2, 124–134 (2015). [CrossRef]  

34. W. J. Choi, K. J. Mohler, B. Potsaid, C. D. Lu, J. J. Liu, V. Jayaraman, A. E. Cable, J. S. Duker, R. Huber, and J. G. Fujimoto, “Choriocapillaris and choroidal microvasculature imaging with ultrahigh speed OCT angiography,” PLOS One 8, e81499 (2013). [CrossRef]  

35. B. Jaeken and P. Artal, “Optical quality of emmetropic and myopic eyes in the periphery measured with high-angular resolution,” Invest. Ophthalmol. Vis. Sci. 53, 3405–3413 (2012). [CrossRef]  

References

  • View by:

  1. D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, “Optical coherence tomography,” Science 254, 1178–1181 (1991).
    [Crossref]
  2. M. Reddikumar, A. Tanabe, N. Hashimoto, and B. Cense, “Optical coherence tomography with a 2.8-mm beam diameter and sensorless defocus and astigmatism correction,” J. Biomed. Opt. 22, 26005 (2017).
    [Crossref]
  3. L. N. Thibos, X. Hong, A. Bradley, and X. Cheng, “Statistical variation of aberration structure and image quality in a normal population of healthy eyes,” J. Opt. Soc. Am. A 19, 2329–2348 (2002).
    [Crossref]
  4. J. Liang, D. R. Williams, and D. T. Miller, “Supernormal vision and high-resolution retinal imaging through adaptive optics,” J. Opt. Soc. Am. A 14, 2884–2892 (1997).
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  5. M. Pircher and R. J. Zawadzki, “Review of adaptive optics OCT (AO-OCT): principles and applications for retinal imaging [Invited],” Biomed. Opt. Express 8, 2536–2562 (2017).
    [Crossref]
  6. Z. Liu, J. Tam, O. Saeedi, and D. X. Hammer, “Trans-retinal cellular imaging with multimodal adaptive optics,” Biomed. Opt. Express 9, 4246–4262 (2018).
    [Crossref]
  7. S. A. Burns, A. E. Elsner, K. A. Sapoznik, R. L. Warner, and T. J. Gast, “Adaptive optics imaging of the human retina,” Prog. Retin. Eye Res. 68, 1–30 (2019).
    [Crossref]
  8. K. Kurokawa, J. A. Crowell, N. Do, J. J. Lee, and D. T. Miller, “Multi-reference global registration of individual A-lines in adaptive optics optical coherence tomography retinal images,” J. Biomed. Opt. 26, 016001 (2021).
    [Crossref]
  9. Y. Jian, S. Lee, M. J. Ju, M. Heisler, W. Ding, R. J. Zawadzki, S. Bonora, and M. V. Sarunic, “Lens-based wavefront sensorless adaptive optics swept source OCT,” Sci. Rep. 6, 27620 (2016).
    [Crossref]
  10. R. Maddipatla, J. Cervantes, Y. Otani, and B. Cense, “Retinal imaging with optical coherence tomography and low-loss adaptive optics using a 2.8-mm beam size,” J. Biophoton. 12, e201800192 (2019).
    [Crossref]
  11. B. Hermann, E. J. Fernández, A. Unterhuber, H. Sattmann, A. F. Fercher, W. Drexler, P. M. Prieto, and P. Artal, “Adaptive-optics ultrahigh-resolution optical coherence tomography,” Opt. Lett. 29, 2142–2144 (2004).
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  12. W. Benjamin, Borish’s Clinical Refraction, 2nd ed. (Elsevier, 2006).
  13. L. W. Alvarez, “Two-element variable-power spherical lens,” U.S. patent application 3,305,294 (3December1964).
  14. W. E. Humphrey, “A remote subjective refractor employing continuously variable sphere-cylinder corrections,” Opt. Eng. 15, 154286 (1976).
    [Crossref]
  15. J. Arines and E. Acosta, “Low-cost adaptive astigmatism compensator for improvement of eye fundus camera,” Opt. Lett. 36, 4164–4166 (2011).
    [Crossref]
  16. J. A. Picazo-Bueno, M. Trusiak, and V. Micó, “Single-shot slightly off-axis digital holographic microscopy with add-on module based on beamsplitter cube,” Opt. Express 27, 5655–5669 (2019).
    [Crossref]
  17. S. Ferrer-Altabás and V. Micó, “Characterization of a compact low-cost Stokes lens for astigmatism compensation in optical instruments,” Appl. Opt. 59, 3347–3352 (2020).
    [Crossref]
  18. A. Camino, R. Ng, J. Huang, Y. Guo, S. Ni, Y. Jia, D. Huang, and Y. Jian, “Depth-resolved optimization of a real-time sensorless adaptive optics optical coherence tomography,” Opt. Lett. 45, 2612–2615 (2020).
    [Crossref]
  19. J. Polans, B. Keller, O. M. Carrasco-Zevallos, F. LaRocca, E. Cole, H. E. Whitson, E. M. Lad, S. Farsiu, and J. A. Izatt, “Wide-field retinal optical coherence tomography with wavefront sensorless adaptive optics for enhanced imaging of targeted regions,” Biomed. Opt. Express 8, 16–37 (2017).
    [Crossref]
  20. K. Zhou, S. Song, Q. Zhang, Z. Chu, Z. Huang, and R. K. Wang, “Visualizing choriocapillaris using swept-source optical coherence tomography angiography with various probe beam sizes,” Biomed. Opt. Express 10, 2847–2860 (2019).
    [Crossref]
  21. N. A. Alpins, “A new method of analyzing vectors for changes in astigmatism,” J. Cataract Refractive Surg. 19, 524–533 (1993).
    [Crossref]
  22. A. Agrawal, T. J. Pfefer, P. D. Woolliams, P. H. Tomlins, and G. Nehmetallah, “Methods to assess sensitivity of optical coherence tomography systems,” Biomed. Opt. Express 8, 902–917 (2017).
    [Crossref]
  23. A. M. McKendrick and N. A. Brennan, “Distribution of astigmatism in the adult population,” J. Opt. Soc. Am. A 13, 206–214 (1996).
    [Crossref]
  24. S. A. Read, S. J. Vincent, and M. J. Collins, “The visual and functional impacts of astigmatism and its clinical management,” Ophthal. Physiol. Opt. 34, 267–294 (2014).
    [Crossref]
  25. N. Pontikos, S. Chua, P. J. Foster, S. J. Tuft, and A. C. Day, and UK Biobank Eye and Vision Consortium, “Frequency and distribution of corneal astigmatism and keratometry features in adult life: methodology and findings of the UK Biobank study,” PLOS One 14, e0218144 (2019).
    [Crossref]
  26. L. R. De Pretto, E. M. Moult, A. Y. Alibhai, O. M. Carrasco-Zevallos, S. Chen, B. Lee, A. J. Witkin, C. R. Baumal, E. Reichel, A. Z. de Freitas, J. S. Duker, N. K. Waheed, and J. G. Fujimoto, “Controlling for artifacts in widefield optical coherence tomography angiography measurements of non-perfusion area,” Sci. Rep. 9, 9096 (2019).
    [Crossref]
  27. T. Liu and L. N. Thibos, “Interaction of axial and oblique astigmatism in theoretical and physical eye models,” J. Opt. Soc. Am. A 33, 1723–1734 (2016).
    [Crossref]
  28. B. Potsaid, B. Baumann, D. Huang, S. Barry, A. E. Cable, J. S. Schuman, J. S. Duker, and J. G. Fujimoto, “Ultrahigh speed 1050 nm swept source/Fourier domain OCT retinal and anterior segment imaging at 100,000 to 400,000 axial scans per second,” Opt. Express 18, 20029–20048 (2010).
    [Crossref]
  29. S. G. Adie, B. W. Graf, A. Ahmad, P. S. Carney, and S. A. Boppart, “Computational adaptive optics for broadband optical interferometric tomography of biological tissue,” Proc. Natl. Acad. Sci. USA 109, 7175–7180 (2012).
    [Crossref]
  30. N. D. Shemonski, F. A. South, Y. Z. Liu, S. G. Adie, P. S. Carney, and S. A. Boppart, “Computational high-resolution optical imaging of the living human retina,” Nat. Photonics 9, 440–443 (2015).
    [Crossref]
  31. F. A. South, K. Kurokawa, Z. Liu, Y. Z. Liu, D. T. Miller, and S. A. Boppart, “Combined hardware and computational optical wavefront correction,” Biomed. Opt. Express 9, 2562–2574 (2018).
    [Crossref]
  32. N. Choudhry, J. Golding, M. W. Manry, and R. C. Rao, “Ultra-widefield steering-based spectral-domain optical coherence tomography imaging of the retinal periphery,” Ophthalmology 123, 1368–1374 (2016).
    [Crossref]
  33. J. Polans, B. Jaeken, R. P. McNabb, P. Artal, and J. A. Izatt, “Wide-field optical model of the human eye with asymmetrically tilted and decentered lens that reproduces measured ocular aberrations,” Optica 2, 124–134 (2015).
    [Crossref]
  34. W. J. Choi, K. J. Mohler, B. Potsaid, C. D. Lu, J. J. Liu, V. Jayaraman, A. E. Cable, J. S. Duker, R. Huber, and J. G. Fujimoto, “Choriocapillaris and choroidal microvasculature imaging with ultrahigh speed OCT angiography,” PLOS One 8, e81499 (2013).
    [Crossref]
  35. B. Jaeken and P. Artal, “Optical quality of emmetropic and myopic eyes in the periphery measured with high-angular resolution,” Invest. Ophthalmol. Vis. Sci. 53, 3405–3413 (2012).
    [Crossref]

2021 (1)

K. Kurokawa, J. A. Crowell, N. Do, J. J. Lee, and D. T. Miller, “Multi-reference global registration of individual A-lines in adaptive optics optical coherence tomography retinal images,” J. Biomed. Opt. 26, 016001 (2021).
[Crossref]

2020 (2)

2019 (6)

K. Zhou, S. Song, Q. Zhang, Z. Chu, Z. Huang, and R. K. Wang, “Visualizing choriocapillaris using swept-source optical coherence tomography angiography with various probe beam sizes,” Biomed. Opt. Express 10, 2847–2860 (2019).
[Crossref]

R. Maddipatla, J. Cervantes, Y. Otani, and B. Cense, “Retinal imaging with optical coherence tomography and low-loss adaptive optics using a 2.8-mm beam size,” J. Biophoton. 12, e201800192 (2019).
[Crossref]

J. A. Picazo-Bueno, M. Trusiak, and V. Micó, “Single-shot slightly off-axis digital holographic microscopy with add-on module based on beamsplitter cube,” Opt. Express 27, 5655–5669 (2019).
[Crossref]

S. A. Burns, A. E. Elsner, K. A. Sapoznik, R. L. Warner, and T. J. Gast, “Adaptive optics imaging of the human retina,” Prog. Retin. Eye Res. 68, 1–30 (2019).
[Crossref]

N. Pontikos, S. Chua, P. J. Foster, S. J. Tuft, and A. C. Day, and UK Biobank Eye and Vision Consortium, “Frequency and distribution of corneal astigmatism and keratometry features in adult life: methodology and findings of the UK Biobank study,” PLOS One 14, e0218144 (2019).
[Crossref]

L. R. De Pretto, E. M. Moult, A. Y. Alibhai, O. M. Carrasco-Zevallos, S. Chen, B. Lee, A. J. Witkin, C. R. Baumal, E. Reichel, A. Z. de Freitas, J. S. Duker, N. K. Waheed, and J. G. Fujimoto, “Controlling for artifacts in widefield optical coherence tomography angiography measurements of non-perfusion area,” Sci. Rep. 9, 9096 (2019).
[Crossref]

2018 (2)

2017 (4)

2016 (3)

T. Liu and L. N. Thibos, “Interaction of axial and oblique astigmatism in theoretical and physical eye models,” J. Opt. Soc. Am. A 33, 1723–1734 (2016).
[Crossref]

N. Choudhry, J. Golding, M. W. Manry, and R. C. Rao, “Ultra-widefield steering-based spectral-domain optical coherence tomography imaging of the retinal periphery,” Ophthalmology 123, 1368–1374 (2016).
[Crossref]

Y. Jian, S. Lee, M. J. Ju, M. Heisler, W. Ding, R. J. Zawadzki, S. Bonora, and M. V. Sarunic, “Lens-based wavefront sensorless adaptive optics swept source OCT,” Sci. Rep. 6, 27620 (2016).
[Crossref]

2015 (2)

J. Polans, B. Jaeken, R. P. McNabb, P. Artal, and J. A. Izatt, “Wide-field optical model of the human eye with asymmetrically tilted and decentered lens that reproduces measured ocular aberrations,” Optica 2, 124–134 (2015).
[Crossref]

N. D. Shemonski, F. A. South, Y. Z. Liu, S. G. Adie, P. S. Carney, and S. A. Boppart, “Computational high-resolution optical imaging of the living human retina,” Nat. Photonics 9, 440–443 (2015).
[Crossref]

2014 (1)

S. A. Read, S. J. Vincent, and M. J. Collins, “The visual and functional impacts of astigmatism and its clinical management,” Ophthal. Physiol. Opt. 34, 267–294 (2014).
[Crossref]

2013 (1)

W. J. Choi, K. J. Mohler, B. Potsaid, C. D. Lu, J. J. Liu, V. Jayaraman, A. E. Cable, J. S. Duker, R. Huber, and J. G. Fujimoto, “Choriocapillaris and choroidal microvasculature imaging with ultrahigh speed OCT angiography,” PLOS One 8, e81499 (2013).
[Crossref]

2012 (2)

B. Jaeken and P. Artal, “Optical quality of emmetropic and myopic eyes in the periphery measured with high-angular resolution,” Invest. Ophthalmol. Vis. Sci. 53, 3405–3413 (2012).
[Crossref]

S. G. Adie, B. W. Graf, A. Ahmad, P. S. Carney, and S. A. Boppart, “Computational adaptive optics for broadband optical interferometric tomography of biological tissue,” Proc. Natl. Acad. Sci. USA 109, 7175–7180 (2012).
[Crossref]

2011 (1)

2010 (1)

2004 (1)

2002 (1)

1997 (1)

1996 (1)

1993 (1)

N. A. Alpins, “A new method of analyzing vectors for changes in astigmatism,” J. Cataract Refractive Surg. 19, 524–533 (1993).
[Crossref]

1991 (1)

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, “Optical coherence tomography,” Science 254, 1178–1181 (1991).
[Crossref]

1976 (1)

W. E. Humphrey, “A remote subjective refractor employing continuously variable sphere-cylinder corrections,” Opt. Eng. 15, 154286 (1976).
[Crossref]

Acosta, E.

Adie, S. G.

N. D. Shemonski, F. A. South, Y. Z. Liu, S. G. Adie, P. S. Carney, and S. A. Boppart, “Computational high-resolution optical imaging of the living human retina,” Nat. Photonics 9, 440–443 (2015).
[Crossref]

S. G. Adie, B. W. Graf, A. Ahmad, P. S. Carney, and S. A. Boppart, “Computational adaptive optics for broadband optical interferometric tomography of biological tissue,” Proc. Natl. Acad. Sci. USA 109, 7175–7180 (2012).
[Crossref]

Agrawal, A.

Ahmad, A.

S. G. Adie, B. W. Graf, A. Ahmad, P. S. Carney, and S. A. Boppart, “Computational adaptive optics for broadband optical interferometric tomography of biological tissue,” Proc. Natl. Acad. Sci. USA 109, 7175–7180 (2012).
[Crossref]

Alibhai, A. Y.

L. R. De Pretto, E. M. Moult, A. Y. Alibhai, O. M. Carrasco-Zevallos, S. Chen, B. Lee, A. J. Witkin, C. R. Baumal, E. Reichel, A. Z. de Freitas, J. S. Duker, N. K. Waheed, and J. G. Fujimoto, “Controlling for artifacts in widefield optical coherence tomography angiography measurements of non-perfusion area,” Sci. Rep. 9, 9096 (2019).
[Crossref]

Alpins, N. A.

N. A. Alpins, “A new method of analyzing vectors for changes in astigmatism,” J. Cataract Refractive Surg. 19, 524–533 (1993).
[Crossref]

Alvarez, L. W.

L. W. Alvarez, “Two-element variable-power spherical lens,” U.S. patent application 3,305,294 (3December1964).

Arines, J.

Artal, P.

Barry, S.

Baumal, C. R.

L. R. De Pretto, E. M. Moult, A. Y. Alibhai, O. M. Carrasco-Zevallos, S. Chen, B. Lee, A. J. Witkin, C. R. Baumal, E. Reichel, A. Z. de Freitas, J. S. Duker, N. K. Waheed, and J. G. Fujimoto, “Controlling for artifacts in widefield optical coherence tomography angiography measurements of non-perfusion area,” Sci. Rep. 9, 9096 (2019).
[Crossref]

Baumann, B.

Benjamin, W.

W. Benjamin, Borish’s Clinical Refraction, 2nd ed. (Elsevier, 2006).

Bonora, S.

Y. Jian, S. Lee, M. J. Ju, M. Heisler, W. Ding, R. J. Zawadzki, S. Bonora, and M. V. Sarunic, “Lens-based wavefront sensorless adaptive optics swept source OCT,” Sci. Rep. 6, 27620 (2016).
[Crossref]

Boppart, S. A.

F. A. South, K. Kurokawa, Z. Liu, Y. Z. Liu, D. T. Miller, and S. A. Boppart, “Combined hardware and computational optical wavefront correction,” Biomed. Opt. Express 9, 2562–2574 (2018).
[Crossref]

N. D. Shemonski, F. A. South, Y. Z. Liu, S. G. Adie, P. S. Carney, and S. A. Boppart, “Computational high-resolution optical imaging of the living human retina,” Nat. Photonics 9, 440–443 (2015).
[Crossref]

S. G. Adie, B. W. Graf, A. Ahmad, P. S. Carney, and S. A. Boppart, “Computational adaptive optics for broadband optical interferometric tomography of biological tissue,” Proc. Natl. Acad. Sci. USA 109, 7175–7180 (2012).
[Crossref]

Bradley, A.

Brennan, N. A.

Burns, S. A.

S. A. Burns, A. E. Elsner, K. A. Sapoznik, R. L. Warner, and T. J. Gast, “Adaptive optics imaging of the human retina,” Prog. Retin. Eye Res. 68, 1–30 (2019).
[Crossref]

Cable, A. E.

W. J. Choi, K. J. Mohler, B. Potsaid, C. D. Lu, J. J. Liu, V. Jayaraman, A. E. Cable, J. S. Duker, R. Huber, and J. G. Fujimoto, “Choriocapillaris and choroidal microvasculature imaging with ultrahigh speed OCT angiography,” PLOS One 8, e81499 (2013).
[Crossref]

B. Potsaid, B. Baumann, D. Huang, S. Barry, A. E. Cable, J. S. Schuman, J. S. Duker, and J. G. Fujimoto, “Ultrahigh speed 1050 nm swept source/Fourier domain OCT retinal and anterior segment imaging at 100,000 to 400,000 axial scans per second,” Opt. Express 18, 20029–20048 (2010).
[Crossref]

Camino, A.

Carney, P. S.

N. D. Shemonski, F. A. South, Y. Z. Liu, S. G. Adie, P. S. Carney, and S. A. Boppart, “Computational high-resolution optical imaging of the living human retina,” Nat. Photonics 9, 440–443 (2015).
[Crossref]

S. G. Adie, B. W. Graf, A. Ahmad, P. S. Carney, and S. A. Boppart, “Computational adaptive optics for broadband optical interferometric tomography of biological tissue,” Proc. Natl. Acad. Sci. USA 109, 7175–7180 (2012).
[Crossref]

Carrasco-Zevallos, O. M.

L. R. De Pretto, E. M. Moult, A. Y. Alibhai, O. M. Carrasco-Zevallos, S. Chen, B. Lee, A. J. Witkin, C. R. Baumal, E. Reichel, A. Z. de Freitas, J. S. Duker, N. K. Waheed, and J. G. Fujimoto, “Controlling for artifacts in widefield optical coherence tomography angiography measurements of non-perfusion area,” Sci. Rep. 9, 9096 (2019).
[Crossref]

J. Polans, B. Keller, O. M. Carrasco-Zevallos, F. LaRocca, E. Cole, H. E. Whitson, E. M. Lad, S. Farsiu, and J. A. Izatt, “Wide-field retinal optical coherence tomography with wavefront sensorless adaptive optics for enhanced imaging of targeted regions,” Biomed. Opt. Express 8, 16–37 (2017).
[Crossref]

Cense, B.

R. Maddipatla, J. Cervantes, Y. Otani, and B. Cense, “Retinal imaging with optical coherence tomography and low-loss adaptive optics using a 2.8-mm beam size,” J. Biophoton. 12, e201800192 (2019).
[Crossref]

M. Reddikumar, A. Tanabe, N. Hashimoto, and B. Cense, “Optical coherence tomography with a 2.8-mm beam diameter and sensorless defocus and astigmatism correction,” J. Biomed. Opt. 22, 26005 (2017).
[Crossref]

Cervantes, J.

R. Maddipatla, J. Cervantes, Y. Otani, and B. Cense, “Retinal imaging with optical coherence tomography and low-loss adaptive optics using a 2.8-mm beam size,” J. Biophoton. 12, e201800192 (2019).
[Crossref]

Chang, W.

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, “Optical coherence tomography,” Science 254, 1178–1181 (1991).
[Crossref]

Chen, S.

L. R. De Pretto, E. M. Moult, A. Y. Alibhai, O. M. Carrasco-Zevallos, S. Chen, B. Lee, A. J. Witkin, C. R. Baumal, E. Reichel, A. Z. de Freitas, J. S. Duker, N. K. Waheed, and J. G. Fujimoto, “Controlling for artifacts in widefield optical coherence tomography angiography measurements of non-perfusion area,” Sci. Rep. 9, 9096 (2019).
[Crossref]

Cheng, X.

Choi, W. J.

W. J. Choi, K. J. Mohler, B. Potsaid, C. D. Lu, J. J. Liu, V. Jayaraman, A. E. Cable, J. S. Duker, R. Huber, and J. G. Fujimoto, “Choriocapillaris and choroidal microvasculature imaging with ultrahigh speed OCT angiography,” PLOS One 8, e81499 (2013).
[Crossref]

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N. Choudhry, J. Golding, M. W. Manry, and R. C. Rao, “Ultra-widefield steering-based spectral-domain optical coherence tomography imaging of the retinal periphery,” Ophthalmology 123, 1368–1374 (2016).
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Appl. Opt. (1)

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Data Availability

Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.

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Figures (8)

Fig. 1.
Fig. 1. Schematic of (a) the OCT sample arm, which equips a VCC and (b) the rotation angles ${A_{\rm VCC1}}$ , ${A_{\rm VCC2}}$ , and ${A_{{\rm VCC}}}$ . The astigmatism generated by the VCC is determined by the rotation angles and cylindricities of two lenses. The VCC was placed in a pupil conjugate plane and relayed to the pupil at a magnification ( $\beta$ ).
Fig. 2.
Fig. 2. Contour plots of the squared total cylindrical power ( $C_{{\rm total}}^2$ ) calculated as a function of ${C_{{\rm VCC}}}$ and ${A_{{\rm VCC}}}$ in the cases where ( $C_{{\rm eye}}$ , ${A_{{\rm eye}}}$ ) = (a) ( ${-}{0.5}\;{\rm D}$ , 135 deg); (b) ( ${-}{2.0}\;{\rm D}$ , 180 deg); and (c) ( ${-}{5.0}\;{\rm D}$ , 45 deg).
Fig. 3.
Fig. 3. Outputs of the merit function as a function of scanning the cylindrical axis ${A_{{\rm VCC}}}$ from 0 deg to 180 deg and the cylindrical power ${C_{{\rm VCC}}}$ approximately from 0 to ${-}{7.0}\;{\rm D}$ for three types of astigmatic model eyes. (a) ( $C_{{\rm eye}}$ , ${A_{{\rm eye}}}$ ) = ( ${-}{0.5}\;{\rm D}$ , 135 deg); (b) ( $C_{{\rm eye}}$ , ${A_{{\rm eye}}}$ ) = ( ${-}{2.0}\;{\rm D}$ , 180 deg); and (c) ( $C_{{\rm eye}}$ , ${A_{{\rm eye}}}$ ) = ( ${-}{5.0}\;{\rm D}$ , 45 deg). In each case, first, ${A_{{\rm VCC}}}$ was scanned with fixed set of ${C_c} = - {1.5}\;{\rm D}$ . ${A_{{\rm VCC}}}$ value that maximizes the merit function ( ${A_{{\rm opt}}}$ ) are indicated in red and arrows. Subsequently, ${C_{{\rm VCC}}}$ was scanned with the fixed parameter of the ${A_{{\rm opt}}}$ . ${C_{{\rm VCC}}}$ value that maximizes the merit function ( ${C_{{\rm opt}}}$ ) are indicated in light blue and arrows.
Fig. 4.
Fig. 4. Scatterplots of the correlation between the trial lens setting on the model eye ( $C_{{\rm eye}}$ , ${A_{{\rm eye}}}$ ) and the value obtained by the VCC optimization process ( ${C_{{\rm opt}}}$ , ${A_{{\rm opt}}}$ ) for (a) cylindrical power and (b) cylindrical axis. The dashed lines indicate the ideal values.
Fig. 5.
Fig. 5. Variations in the relative SNR of the OCT signal. The relative SNR with VCC is set to 0 at the point $C_{{\rm eye}} = {0.0}\;{\rm D}$ . The dashed line shows the linear relationship between cylindrical power and relative SNR with a slope ${-}{4.4}$ .
Fig. 6.
Fig. 6. OCT images of the microbeads model eye. (a) OCT B-scan image of a model eye; (b)–(d) comparison between OCT en face projections ( ${1}\;{\rm mm} \times {1}\;{\rm mm}$ , ${512}\;{\rm pixels} \times {512}\;{\rm pixels}$ ) of the microbeads layer when ${C_{{\rm VCC}}} = {0}$ (VCC OFF) and after VCC astigmatism correction (VCC ON). The refractive properties of the model eye are (b) ( ${-}{0.5}\;{\rm D}$ , 135 deg); (c) ( ${-}{2.0}\;{\rm D}$ , 180 deg); and (d) ( ${-}{5.0}\;{\rm D}$ , 45 deg). Bar: 200 µm.
Fig. 7.
Fig. 7. (a), (b) Data set for the astigmatic eye of ( $C_{{\rm eye}}$ , ${A_{{\rm eye}}}$ ) = ( ${-}{1.6}\;{\rm D}$ , 104 deg). (a) Changes in merit function during the search for ${A_{{\rm opt}}}$ and ${C_{{\rm opt}}}$ in the astigmatic human eye; (b) OCTA images ( ${3}\;{\rm mm} \times {3}\;{\rm mm}$ , ${512}\;{\rm pixels} \times {512}\;{\rm pixels}$ , five repetitions) of the superficial layer captured when ${C_{{\rm VCC}}} = {0}$ (VCC OFF) and after VCC astigmatism correction (VCC ON). (c), (d) Data set for the astigmatic eye of ( $C_{{\rm eye}}$ , ${A_{{\rm eye}}}$ ) = ( ${-}{4.3}\;{\rm D}$ , 99 deg) obtained in the same manner. Bar: 200 µm.
Fig. 8.
Fig. 8. OCT images of the emmetropic human eye at a region 30 deg from the macular center. OCT B-scan with segmentation boundaries and OCT en face projections ( ${1}\;{\rm mm} \times {1}\;{\rm mm}$ , ${512}\;{\rm pixels} \times {512}\;{\rm pixels}$ ) near the IS/OS junction when (a)  ${C_{{\rm VCC}}} = {0}$ (VCC OFF) and (b) after VCC astigmatism correction (VCC ON). Bar: 200 µm.

Equations (2)

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C V C C = 2 C V C C 1 β 2 cos ( A V C C 2 A V C C 1 ) A V C C = A V C C 1 + A V C C 2 2 ,
C t o t a l 2 = ( C e y e cos 2 A e y e C V C C cos 2 A V C C ) 2 + ( C e y e sin 2 A e y e C V C C sin 2 A V C C ) 2 = C V C C 2 2 C V C C C e y e cos 2 ( A V C C A e y e ) + C e y e 2 ,

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